I personally don't like training chest and back on the same day because it requires serious effort and I don't think you get maximum results, though I have done days every once in a while where I've supersetted chest and back and those days tend to be brutal. My feeling is that you probably shouldn't need more protein on that day, but that opinion is more out of the "eat as much protein everyday" school of thought than anything scientific. If anything, a workout that demanding might require more carbs for the energy expenditure. If you are counting every last calorie, you should probably listen to the other bros about your question, though.